Question

derive Laplace's law for spherical membrane.Physics - Surface Tension

Answer 1

According to this law the difference between the pressure of inner and outer surfaces of a spherical membrane is expressed as
P in - P out = 2T/r

under the equilibrium conditions
Force due to excess pressure = force due to surface tension
P in - P out (pie r )² = T (2pie/r)
(P in - P out) r = 2T
P in - P out= 2T/r

Answer 2

Explanation:

Laplace's Law of a Spherical Membrane for a Liquid Bubble:

Let the radius of the bubble increases from r to r + Δr, where Δr is very very small, hence the inside pressure is assumed to be constant.